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Shortcut Tricks: Sequences Video Lecture | Quantitative for GMAT
FAQs on Shortcut Tricks: Sequences Video Lecture - Quantitative for GMAT
| 1. What is an arithmetic progression (AP) and how is it defined? |  |
Ans.An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference, denoted as 'd'. The nth term of an AP can be expressed as: \( a_n = a + (n - 1)d \), where 'a' is the first term and 'n' is the term number.
| 2. How do you find the sum of the first n terms in an arithmetic progression? | |
Ans.The sum of the first n terms (S_n) of an arithmetic progression can be calculated using the formula: \( S_n = \frac{n}{2} (2a + (n - 1)d) \) or \( S_n = \frac{n}{2} (a + l) \), where 'l' is the last term. This formula helps in quickly calculating the sum without needing to add each individual term.
| 3. What are some practical applications of arithmetic progressions? | |
Ans.Arithmetic progressions are used in various fields such as finance (calculating installment payments), computer science (algorithms), and physics (motion problems). They are also applicable in real-life situations like determining seating arrangements or scheduling events at regular intervals.
| 4. Can you provide an example of an arithmetic progression? | |
Ans.An example of an arithmetic progression is the sequence 2, 5, 8, 11, 14, ... Here, the first term (a) is 2, and the common difference (d) is 3. The sequence can be extended indefinitely by continuing to add the common difference to the last term.
| 5. How do you determine if a sequence is an arithmetic progression? | |
Ans.To determine if a sequence is an arithmetic progression, calculate the differences between consecutive terms. If all the differences are the same (i.e., they all equal the common difference 'd'), then the sequence is an AP. For example, in the sequence 3, 6, 9, the differences are 3, which confirms it is an arithmetic progression.
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